On the characterization of some families of closed convex sets
The authors obtain characterizations of simplices, sandwiches (convex hulls of pairs of parallel affine manifolds), parallelotopes and sums of compact convex sets with linear subspaces in terms of their internal and conical representations. They also provide characterizations of some of these interesting families of sets using visibility properties of their boundary points and prove that a closed convex set is a sandwich if and only if its relative boundary is not connected. Applications of some of these characterizations are also studied and it is proved that a bounded linear semi-infinite programming problem whose feasible set is the sum of a compact convex set with a linear subspace is necessarily solvable and has zero duality gap.
scientific article; zbMATH DE number 1784599